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- Fiber_bundle abstract "In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space E and a product space B × F is defined using a continuous surjective map that in small regions of E behaves just like a projection from corresponding regions of B × F to B. The map π, called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space E is known as the total space of the fiber bundle, B as the base space, and F the fiber.In the trivial case, E is just B × F, and the map π is just the projection from the product space to the first factor. This is called a trivial bundle. Examples of non-trivial fiber bundles include the Möbius strip and Klein bottle, as well as nontrivial covering spaces. Fiber bundles such as the tangent bundle of a manifold and more general vector bundles play an important role in differential geometry and differential topology, as do principal bundles.Mappings which factor over the projection map are known as bundle maps, and the set of fiber bundles forms a category with respect to such mappings. A bundle map from the base space itself (with the identity mapping as projection) to E is called a section of E. Fiber bundles can be generalized in a number of ways, the most common of which is requiring that the transitions between the local trivial patches lie in a certain topological group, known as the structure group, acting on the fiber F.".
- Fiber_bundle thumbnail Roundhairbrush.JPG?width=300.
- Fiber_bundle wikiPageExternalLink FiberBundle.html.
- Fiber_bundle wikiPageExternalLink fibundle.html.
- Fiber_bundle wikiPageExternalLink 0908.1886.
- Fiber_bundle wikiPageID "276526".
- Fiber_bundle wikiPageRevisionID "604317769".
- Fiber_bundle first "M.I.".
- Fiber_bundle hasPhotoCollection Fiber_bundle.
- Fiber_bundle id "F/f040060".
- Fiber_bundle last "Voitsekhovskii".
- Fiber_bundle title "Fiber Bundle".
- Fiber_bundle title "Fibre space".
- Fiber_bundle urlname "FiberBundle".
- Fiber_bundle year "2001".
- Fiber_bundle subject Category:Algebraic_topology.
- Fiber_bundle subject Category:Differential_topology.
- Fiber_bundle subject Category:Fiber_bundles.
- Fiber_bundle subject Category:Homotopy_theory.
- Fiber_bundle comment "In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space E and a product space B × F is defined using a continuous surjective map that in small regions of E behaves just like a projection from corresponding regions of B × F to B.".
- Fiber_bundle label "Espace fibré".
- Fiber_bundle label "Faserbündel".
- Fiber_bundle label "Fiber bundle".
- Fiber_bundle label "Fibrado".
- Fiber_bundle label "Fibrato".
- Fiber_bundle label "Maço de fibras".
- Fiber_bundle label "Vezelbundel".
- Fiber_bundle label "Локально тривиальное расслоение".
- Fiber_bundle label "حزمة ليفية".
- Fiber_bundle label "ファイバー束".
- Fiber_bundle label "纤维丛".
- Fiber_bundle sameAs Faserbündel.
- Fiber_bundle sameAs Fibrado.
- Fiber_bundle sameAs Espace_fibré.
- Fiber_bundle sameAs Fibrato.
- Fiber_bundle sameAs ファイバー束.
- Fiber_bundle sameAs 올다발.
- Fiber_bundle sameAs Vezelbundel.
- Fiber_bundle sameAs Maço_de_fibras.
- Fiber_bundle sameAs m.01pdfw.
- Fiber_bundle sameAs Q1154996.
- Fiber_bundle sameAs Q1154996.
- Fiber_bundle wasDerivedFrom Fiber_bundle?oldid=604317769.
- Fiber_bundle depiction Roundhairbrush.JPG.
- Fiber_bundle isPrimaryTopicOf Fiber_bundle.
